{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Condition number"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import matplotlib.pyplot as pt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let's grab a $2\\times 2$ matrix $A$:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 3.,  0.],\n",
              "       [ 0.,  1.]])"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "if 0:\n",
        "    np.random.seed(17)\n",
        "    A = np.random.randn(2, 2)\n",
        "else:\n",
        "    A = np.array([[3, 0], [0,1]], dtype=np.float64)\n",
        "\n",
        "A"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "And its inverse as `Ainv`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0.33333333,  0.        ],\n",
              "       [ 0.        ,  1.        ]])"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Ainv = la.inv(A)\n",
        "Ainv"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now we would like to figure out where that matrix puts all the vectors with 2-norm 1.\n",
        "\n",
        "To do so, let's make an array of vectors with vectors with norm 1:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAREAAAEACAYAAACUHkKwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmoM+fecAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fb8c2559e80>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "phi = np.linspace(0, 2*np.pi, 30)\n",
        "xs = np.array([\n",
        "    np.cos(phi),\n",
        "    np.sin(phi)\n",
        "])\n",
        "\n",
        "pt.gca().set_aspect(\"equal\")\n",
        "pt.plot(xs[0], xs[1], \"x\")\n",
        "pt.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now apply $A$ to all those vectors...:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(2, 30)"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Axs = A.dot(xs)\n",
        "Axs.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "...and plot:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "image/png": 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89Kt0NVtlWg+A7NW5ZgtAPXS2hZAsKXTuuVdry5YvVLNmCwAAoEx6DYrv++vL9FcYfxUC\nw6duO1uLF6+RRANToG66NT2dN29edZuaAkBV3X//hCQamAJ1M8gJLwRbAJC6dquHm4peCIAUHe4J\nL6nUbNleanub7SdtX9Pl80faXm97u+0f2z4tjecFgDSk/R7Wrueg1QNQL7Z13XWfPOT/2wMHW7bn\nSfqypCWS3iLpEttnzDjsLyU9HxFvlPQFSTcM+rwAkIb038NoYArgQGnsbJ0jaXtE7IyIVyStl7R8\nxjHLJd3Wur5B0vkpPC+AipqYkHbuLHoV01J9Dzv6aBqYAnV21ln/Qcceu0IjI5f2/TVpBFsnS3q6\n4/Yzrfu6HhMReyVN2X5tCs8NoIIuu0y68MLSBFypvodlMcQWQHm85z1n6sUXP6Lf/OYbfX9NUX22\n+JMPGGKnny7ddVcScFVUz/eww6nnAFAda9deo1e/+muS8h3Xs0tSZ7HoKa37Oj0j6VRJv7J9hKRj\nIuL5bg82MTExfb3RaKjRaKSwRABl0Ww21Ww2JUnveIf02GPFrke8hwHoU/v9a9GiF/WTn/xF3183\ncFPT1hvPE0pqGHZLekDSJRHxeMcxV0r69xFxpe2LJV0UERd3eSyamgJDYufOZGfrsceKbWrKexiA\nQ7Vv3z4dc8yYXnrp2/k0NY2IvbY/LukeJWnJdRHxuO3PSnowIu6StE7SN21vl/RrSbPepAAMj3ag\ndddd0oIFxa4l7fewRmOi/bh0kAdqat68ebriinN0003f7ut4xvUAyN3ERFIkf/rp9RvX067jmD9/\nk26/3RobW1LwqgBkYd++fTriiCP6ev8i2AJQqHoGWzE9O41ieaC++n3/KupsRACoLTrIA+jEbEQA\nSBVzEYG6WbVqrbZu/e0Bf0AdSiaOYAsAUkQHeaB+RkcX6ZZbrJdf3l+DOX/+pr6/njQiAKSIDvJA\n/YyNLdGiRZu0v5FpsoPdLwrkARSqbgXyvIcB9bRhwyatWJHsbrXPNv7wh5dyNiKA8qtrsNWrxoPe\nW0A1RYTOO+9qbdly0/TZxvPmzcunqWlWpqakzZulZcuKXgkAHLpeNR5XXVWLuBIYOrb1iU8s0cqV\nh16XWcqarakpafVqaXS06JUAwOHpVeNBPRdQXWNjSw6rLrN0acTJydDatdK110ojI0WvCEDW6ppG\nlLrXeNBRHqiPft+/ShdsSaHJyeLnpQHIR52DrW41HrSEAOqj3/ev0tVsTU6KnS0AtTBIjQeA/GR9\nQkvpgq0FC5JAa/VqAi4A2bJ9nKR/lHS6pB2SPhIRv+ly3F5J/yrJknZGxEX9PsfY2BI99NAj1GoB\nJZb1CS2lSyO218PZiMBwKDKNaPt6Sb+OiBtsXyPpuIj4VJfjXoyIY/p4PNrXABXUmfJP/qbqb5h8\n5QdRj4wQaAHI3HJJt7Wu3yap144V+T+gxtop//nz75GU/jD50u5sARgOBe9sPR8Rr+11u+P+30l6\nWNL/k3R9RHynx+Md9nsYTVCBYh3OCS2VLZAHgDTZvlfSiZ13KWl+9Zkuh/eKlE6PiN22F0q6z/Yj\nETGZ5jppggoUK8sTWgi2ANRaRLy31+ds77F9YkTssX2SpOd6PMbu1sdJ201JZ0nqGmxNTExMX280\nGmo0Gn2tc2xsiW688Wpt2fI+tePBpAnqTX19PYDBHeyElmazqWazeciPSxoRQKFKUCD/fERc36tA\n3vaIpJcj4ne2j5e0WdLyiNjW5fEGeg+jCSpQLZVtalqm9QDIXsHB1mslfUvSqZJ2Kmn9MGX77ZKu\niIjLbZ8n6WZJe5WcVPT5iPhGj8cb6D2MJqjAYPKufaRmC0CpbNyYzDvt7J03NVXceiQpIp6X9Kdd\n7v+ppMtb138s6a15rIcmqMBgylr7WNrWDwDqZXQ0aVbcDrDaA+dxoMMddAugvAPgSSMCyE07wBof\n3z+W67jj6jsbMW+0jwDyrX2kZgtAKe3YIS1cqOmB83UeRJ23zl8ybRTaY9jkWftY+Q7yAOpnairZ\n0WoPnC+6ZqtuyppCAfLUrn08+ujy1D5SIA8gF+0UYnvAfHvgPNLT/iWzYsU9rRRKuiNHgCxkkf4u\n2wB40ogActHrbERqttJF+whUTZXT36QRAZTKsmUHBlrS7NsYXBlTKMBchiH9TRoRAGomrRQKZzci\nD8OQ/iaNCKBQnI1YXlVO76Baqpr+pvUDgEog2Cqvzl+A7eHYVfpFiPTkscu5YcMmrVx5t269dWll\ngnnG9QAABjIM6R30J48xOGU7gzBN7GwBKBQ7W+WWdXqHurBqYJezu1qcjbhx4+ymh1NTyf0AMCjb\nH7b9mO29ts+e47iltrfZftL2NXmusWhZn904OrpIDz30Lt1//8T05aGHztO7353L7G/0qf3vYP78\neySJXc5DVOpgq9fg2tHRYtcFoDYelfRBSff3OsD2PElflrRE0lskXWL7jHyWl41ms3lIx2c5HHuu\n0/4PdZ1FKnKtq1at1eLFa9RoTExfFi9eo1Wr1s46dpB1dr5WWbdmqNJr349S12x1dpnuHFxLbx4A\naYiIJyTJc/95fo6k7RGxs3XseknLJW3LfoXZaDabajQafR9vW9dd98lM1jJXXdihrnMuWacrO9ea\nd2r0UOqpBvmZtl+rlSuz7+GW5mtfBqUOtqQksBof3z+4lkALQM5OlvR0x+1nlARgSMnY2BLdeOPV\n2rLlfa0dk5tSf448CryLeC7pwJ9fu54qq59jnYvYs1TqNKLE4FoAg7F9r+1HOi6Ptj7+WdFrQyKP\nrvd5dinPuyN6nvVU7V1OarUOTanPRpw5uHbmbQDVV4azEW3/i6S/iYitXT73TkkTEbG0dftTkiIi\nru9ybHneUAHkovJNTXsNrt28OZmzBqD6ShRsfSIiftrlc0dIekLS+ZJ2S3pA0iUR8Xi+qwRQVaUO\ntgDUX5HBlu2LJP2dpOMlTUl6OCIusP06SX8fERe2jlsq6YtKSi/WRcR1RawXQDURbAEoVBl2tgAg\nS6UvkAeAKrH9323/q+2f2d5k+6Si19SN7RtsP277Ydv/0/YxRa+pm34bzxalKg1vba+zvcf2I0Wv\nZS62T7F9n+2ft05muaroNXVj+yjbW1r/zx+1vWbO48u0k8TOFjB86razZfs1EfHb1vW/lvTHEfFX\nBS9rFtt/Kum+iNhn+zolRf+fLnpdM9l+s6R9km5WUlc36ySGorQa3j6ppJ7vV5IelHRxRJSuB5vt\nd0v6raTbI6K07flbf5ycFBEP236NpJ9KWl7Sn+n8iHi5Vde5WdJVEfFAt2PZ2QKAFLUDrZZXKwkU\nSicivh8R7bX9RNIpRa6nl4h4IiK2K2kgVTbTDW8j4hVJ7Ya3pRMRP5T0QtHrOJiIeDYiHm5d/62k\nx5X0uiudiHi5dfUoJX1Le+4WEWwBQMps/63tpyR9VNJ/K3o9fVgp6XtFL6KCujW8LWVgUEW2F0g6\nU9KWYlfSne15tn8m6VlJ90bEg72OJdgCMLBhGxp/sEapEfGZiDhN0j9I+uuyrrN1zGpJr0TEHWVe\nJ4ZLK4W4QdJ/nrFbXBoRsS8izlKyK3yu7T/udWzpx/UAKL/20PhuDYjrKCLe2+ehd0j6rqSJ7FbT\n28HWaftSSe+X9J5cFtTDIfw8y2aXpNM6bp/Sug8DsP0qJYHWNyPiO0Wv52Ai4sVWr76lkn7R7Rh2\ntgAMrHNo/I4dwz3pwfYbOm5epKTmpHRavcPGJX0gIv5v0evpU9nqth6U9Abbp9s+UtLFku4seE1z\nscr3M+zm65J+ERFfLHohvdg+3vaxreu/L+m9mmM4PWcjAkjNjh37h8YvWNDf19TwbMQNkt6kpDB+\np6T/GBG7i13VbLa3SzpS0q9bd/0kIq4scEld9Wo8W+yq9qtKw1vbd0hqSPoDSXskrYmIWwtdVBe2\nRyX9QNKjSgrOQ9J/jYhNhS5sBtuLJN2m5HWfJ+kfI6LnXj7BFoBUtFOH4+PJ0Ph+d7bqFmwBwEyk\nEQEMrLNGa8GC/SnFmUXzADCM2NkCMLBBhsazswWg7gi2ABSKYAtA3Q2URrR9nO17bD9h++52ZX6X\n4/ba3tqaIfTtQZ4TAACgSgba2bJ9vaRfR8QNrQGcx0XEp7oc92JEHHTIKTtbwPBhZwtA3Q0abG2T\ntDgi9rSGRzYj4owux/2fiDi6j8cj2AKGDMEWgLob9GzEEyJij5QMj5R0Qo/jjrL9gO0f2S7lkE4A\nAIAsHHRcj+17JZ3YeZeSJmOf6XJ4r22p0yNit+2Fku6z/UhETB7yag9ikDOiAAAAsnDQYGuumVW2\n99g+sSON+FyPx9jd+jhpuynpLEldg62JiYnp641GQ41G42BLnDZs89mAKmo2m2o2m0UvAwByk0aB\n/PMRcX2vAnnbI5Jejojf2T5e0mZJyyNi1gyhNGq2DreLNYBiULMFoO4GDbZeK+lbkk5VMgPsIxEx\nZfvtkq6IiMttnyfpZkl7ldSIfT4ivtHj8VIpkD+c+WwAikGwBaDuatfUlJ0toFoItgDUXa1mIzKf\nDQAAlE2tdrY4GxGoHna2ANRdrYItANVDsAWg7mqVRgQAACgbgi0AAIAMEWwBAABkiGALAAAgQwRb\nAKZt3Di7VcrUVHI/AODwEGwBmNaeL9oOuNq960ZHi10XAFQZrR8AHCDvKQy0fgBQdwRbAGbJc74o\nwRaAuiONCOAAU1PJjtbkZPKRcVcAMBiCLQDTmC8KAOkjjQhgWhHzRUkjAqg7gi0AhSLYAlB3pBEB\nAAAyRLAFAACQIYKtDnTPBgAAaSPY6kD3bAAAkDYK5GfIu3s2MOwokAdQdwRbXeTZPRsYdgRbAOqO\nNOIMdM8GAABpItjqQPdsAACQNtKIHYrong0MO9KIAOqOYAtAoQi2ANQdaUQAAIAMEWwBAABkiGAL\nqDgmHwBAuRFsARXH5AMAKDcK5IEaqPLkAwrkAdQdwRZQE1WdfECwBaDuSCMCNcDkAwAoL4ItoOKY\nfAAA5UYaEai4qk8+II0IoO4ItgAUimALQN2RRswYPZAAABhuBFsZowcSAADDjTRiDqrcAwnIGmlE\nAHVHsJWTqvZAArJGsAWg7kgj5oAeSAAADC+CrYzRAwkAgOFGGjFjVe+BBGSNNCKAuiPYAnJC4N0d\nwRaAuiONCOSENiAAMJzY2QJyRBuQ2djZAlB3BFtAzmgDciCCLQB1RxoRyBFtQABg+BBsATmhDQgA\nDCeCrYpj0HV1bN58YI3WyEhye/PmYtcFAMgWNVsV17lbMjIy+zZQdtRsAag7gq0a4Aw3VBnBFoC6\nI9iqCc5wQ1URbAGoO2q2aoAz3AZD3RsAIEsEWxXHGW6Do7M7ACBLpBErjnl76aDurTikEQHU3UDB\nlu0PS5qQ9EeS3hERW3sct1TSF5TspK2LiOt7HEewVWJ1D+yoeysGwRaAuhs0jfiopA9Kur/XAbbn\nSfqypCWS3iLpEttnDPi8tdRsNotewpyyTLcV/b0XXfdW9PcPAMjOQMFWRDwREdslzfVX6TmStkfE\nzoh4RdJ6ScsHed66Kvsv3HYTztWrk12gNPt5zfze8yxaL0PdW9lfewDA4cujQP5kSU933H6mdR8q\naGQkqWtauDD5mFVdU55F63R2BwBk6aDBlu17bT/ScXm09fHP8lggyiWvdFuWu2gzLVs2+3FHRupR\nhwYAKF4qZyPa/hdJf9OtQN72OyVNRMTS1u1PSYpuRfK2qY4HhhAF8gDq7FUpPlavN8sHJb3B9umS\ndku6WNIl3Q7kDRcAANTNQDVbti+y/bSkd0q6y/b3Wve/zvZdkhQReyV9XNI9kn4uaX1EPD7YsgEA\nAKqhVE1NAQAA6qbQcT22P2z7Mdt7bZ89x3FLbW+z/aTta/JcY5ZsH2f7HttP2L7b9rE9jttre6vt\nn9n+dt7rTNPBXkvbR9peb3u77R/bPq2IdWahj+99he3nWq/1Vtsri1hnFmyvs73H9iNzHPOl1uv+\nsO0z81wfAGSp6NmIw94U9VOSvh8Rb5Z0n6RP9zjupYg4OyLOioiL8lteuvp8Lf9S0vMR8UYlUwdu\nyHeV2TiEf8frW6/12RHx9VwXma1blXzvXdm+QNLrW6/7FZK+mtfCACBrhQZbNEXVckm3ta7fJqlX\nIFWXEweM/7UIAAACWUlEQVT6eS07fyYbJJ2f4/qy1O+/47q81geIiB9KemGOQ5ZLur117BZJx9o+\nMY+1AUDWit7Z6kedm6KeEBF7JCkinpV0Qo/jjrL9gO0f2a5yoNnPazl9TOvkiinbr81neZnq99/x\nh1pptG/ZPiWfpZXCzJ/PLtXn/zmAIZdm64eubN8rqfMvVEsKSasj4p+zfv6izfH9f6bL4b3OVjg9\nInbbXijpPtuPRMRkykstq1ru9PRwp6Q7IuIV25cr2eGry84eAAytzIOtiHjvgA+xS1JnkfQprfsq\nYa7vv1UwfGJE7LF9kqTnejzG7tbHSdtNSWdJqmKw1c9r+YykUyX9yvYRko6JiOdzWl+WDvq9R0Rn\nmu1rqkm9Wp92KXnd2yr1/xwA5lKmNOJBm6LaPlJJU9Q781tWpu6UdGnr+gpJ35l5gO2R1vct28dL\nepekX+S1wJT181r+s5KfhST9uZITB+rgoN97K+BuW67qvs69WL3/n98p6WPS9NSJqXaKHQCqLvOd\nrbnYvkjS30k6XklT1Icj4gLbr5P09xFxYUTstd1uijpP0roaNUW9XtK3Wqf475T0EUmy/XZJV0TE\n5ZL+SNLNtvcq+f4/FxHbilrwIHq9lrY/K+nBiLhL0jpJ37S9XdKvlQQlldfn936V7Q9IekXS89of\niFee7TskNST9ge2nJK2RdKSS0V23RMR3bb/f9i8lvSTpsuJWCwDpoqkpAABAhsqURgQAAKgdgi0A\nAIAMEWwBAABkiGALAAAgQwRbAAAAGSLYAgAAyBDBFgAAQIYItgAAADL0/wGLb/0yGJ5muAAAAABJ\nRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fb8c1c9b9b0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pt.figure(figsize=(10, 5))\n",
        "\n",
        "pt.subplot(121)\n",
        "pt.title(\"$x$\")\n",
        "pt.plot(xs[0], xs[1], \"x\")\n",
        "pt.gca().set_aspect(\"equal\")\n",
        "\n",
        "pt.subplot(122)\n",
        "pt.title(\"$Ax$\")\n",
        "pt.plot(Axs[0], Axs[1], \"v\")\n",
        "pt.gca().set_aspect(\"equal\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "-------------\n",
        "\n",
        "Next, let's see what happens to small perturbations at each of the $x$ and $Ax$ points.\n",
        "\n",
        "To that end, let's make an array `ys` of shape $2\\times N_p\\times N_p$, where $N_p$ is the number of points above."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(2, 30, 30)"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# ys has axes: XY x Npoints x Npoints\n",
        "\n",
        "perturbation_size = 0.1\n",
        "ys = perturbation_size * xs.reshape(2, -1, 1) + xs.reshape(2, 1, -1)\n",
        "\n",
        "Ays = np.tensordot(A, ys, axes=1)\n",
        "Ays.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Side note: What does the argument `-1` to reshape do?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "-----------------------\n",
        "Let's plot what we've just made"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "image/png": 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+l+S/fjV0BXlnaor3LyHEuanNPcwZPVuHgFYnPY6peu4ErfXxkx6+D7x0thPO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\naCh+fp1ZsGABq1at4pNPPql3HCEhIeTn5/Pcc5rnnjMWk1x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3xihA+zowvTYLHurZnwlI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\nSUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fb8c1bdc5c0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pt.figure(figsize=(10, 5))\n",
        "\n",
        "pt.subplot(121)\n",
        "pt.title(\"$y$\")\n",
        "pt.plot(ys[0], ys[1])\n",
        "pt.gca().set_aspect(\"equal\")\n",
        "\n",
        "pt.subplot(122)\n",
        "pt.title(\"$Ax$\")\n",
        "pt.plot(Ays[0], Ays[1])\n",
        "pt.gca().set_aspect(\"equal\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "-------------------\n",
        "Let's compare this with $\\|A\\|$:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "3.0\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<matplotlib.patches.Circle at 0x7fb8c1b29f28>"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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5WZm98OpgTBPWr4cXXrDTN2+/HYYefI5IUZReELFCPF3xC96sf5TjfF9lZtr5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\nhxBCj/gX2n1UBOi3k5cAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fb8c18de470>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "norm = la.norm(A, 2)\n",
        "print(norm)\n",
        "\n",
        "pt.plot(Ays[0], Ays[1])\n",
        "\n",
        "ax = pt.gca()\n",
        "ax.set_aspect(\"equal\")\n",
        "ax.add_artist(pt.Circle([0, 0], norm, alpha=0.3, lw=0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "------------------\n",
        "What we want now is a circle around each of the $Ax$ that says,\n",
        "\n",
        "\"Because of the $\\Delta x$ variation, $b$ is at most going to wiggle by this much,\n",
        "i.e. $\\Delta b$ will be at most this big.\""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "------\n",
        "\n",
        "Now we want a $\\kappa$ with $\\frac{\\|\\Delta b\\|}{\\|b\\|}\\le \\kappa \\frac{\\|\\Delta x\\|}{\\|x\\|}$.\n",
        "\n",
        "Assume $\\|x\\|=1$. Equivalent: $\\|\\Delta b\\|\\le \\kappa \\|\\Delta x\\|\\|b\\|$.\n",
        "\n",
        "Which $\\kappa$ does the job?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "kappa = la.norm(A, 2)*la.norm(Ainv, 2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "image/png": 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w/MVHSegIdZT+UYWkIWC17HLCRmOrORy1RPgieTKZrF39o1xwbi1rON/nhoaA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\nC3wdHR2dC4T/D2a/jOWiJHN3AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fb8c1ad0ba8>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pt.plot(Ays[0], Ays[1])\n",
        "\n",
        "ax = pt.gca()\n",
        "ax.set_aspect(\"equal\")\n",
        "for i in range(Ays.shape[2]):\n",
        "    b = Axs[:, i]\n",
        "    norm_delta_y = kappa * perturbation_size * la.norm(b)\n",
        "    ax.add_artist(pt.Circle(b, norm_delta_y, alpha=0.3, lw=0))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.5.0+"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}